The Lennard$-$Jones potential model consists of two 'parts'; a steep repulsive term $(1/$r$^12),$ and smoother attractive term $(-1/$r$^6),$ representing van der Waals dispersion forces present in all molecules.

The $12-6$ Lennard$-$Jones model has found widespread use due to its computational expediency. The Lennard$-$Jones potential equation:

V$($r$)=4[(\backslash$sigma $/$r$)^12(\backslash$sigma $/$r$)^6]$

where,

V is the intermolecular potential between the two atoms or molecules.

$$ is the well depth and a measure of how strongly the two particles attract each other.

$\backslash$sigma is the distance at which the intermolecular potential between the two particles is zero $($Figure $3$ provided$).$

$\backslash$sigma gives a measurement of how close two nonbonding particles can get and is thus referred to as the van der Waals radius. It is equal to one$-$half of the internuclear distance between nonbonding particles.

r is the distance of separation between both particles $($measured from the center of one particle to the center of the other particle$).$

The actual force of interaction along a linear direction is given by:

F$($r$)=-$dV$($r$)/$ dr

A$.$ For the given model, at what distance rmin does the minimum occur for interaction potential, V$($r$)$ and force F$($r$)?$